Gibbs ensemble technique

Panagiotopoulos A Z 1995 Gibbs ensemble techniques Observation, Prediction and Simuiation of Phase Transitions in Oompiex Fiuids ed M Baus, L F Rull and J-P Ryckaert, vol 460 NATO ASi Series O (Dordrecht Kluwer) pp 463-501... 

As usual, a problem arises when the Gibbs ensemble technique is applied to a system consisting of pol5mieric molecules. In particular, when a chain molecule is removed from one box and an attempt is made to insert it into the other box (the particle swap move described above), the new configuration almost always... 

The Gibbs-ensemble technique was introduced by Panagio-topoulos as an efficient tool to simulate vapor-liquid phase equilibria. In the Gibbs-ensemble scheme simulations of the liquid and vapor phases are carried out in parallel. Monte Carlo rules which allow for changes in the number of particles and the volume ensure that the two boxes are in thermodynamic... 

Siepmann et al. have used the combination of the Gibbs-ensemble technique and configurational-bias Monte-Carlo to simulate vapor-liquid equilibria of the n-alkanes at conditions where experiments are not (yet) feasible. Phase diagrams are very sensitive to the choice of interaction potentials. Most available models for alkanes have been obtained by fitting simulation data to experimental properties of the liquid under standard conditions. In Figure 6 the vapor- liquid curve of octane as predicted by some of these models is compared with experimental data. This figures shows that the models... 

In this section we review several studies of phase transitions in adsorbed layers. Phase transitions in adsorbed (2D) fluids and in adsorbed layers of molecules are studied with a combination of path integral Monte Carlo, Gibbs ensemble Monte Carlo (GEMC), and finite size scaling techniques. Phase diagrams of fluids with internal quantum states are analyzed. Adsorbed layers of H2 molecules at a full monolayer coverage in the /3 X /3 structure have a higher transition temperature to the disordered phase compared to the system with the heavier D2 molecules this effect is... 

Another method of simulating chemical reactions is to separate the reaction and particle displacement steps. This kind of algorithm has been considered in Refs. 90, 153-156. In particular. Smith and Triska [153] have initiated a new route to simulate chemical equilibria in bulk systems. Their method, being in fact a generalization of the Gibbs ensemble Monte Carlo technique [157], has also been used to study chemical reactions at solid surfaces [90]. However, due to space limitations of the chapter, we have decided not to present these results. 

The first Monte Carlo study of osmotic pressure was carried out by Panagiotopoulos et al. [16], and a much more detailed study was subsequently carried out using a modified method by Murad et al. [17]. The technique is based on a generalization of the Gibbs-ensemble Monte Carlo (GEMC) method applied to membrane equihbria. The Gibbs ensemble method has been described in detail in many recent reports so we will only summarize the extension of the method to membrane equilibria here [17]. In the case of two phases separated by semi-permeable membranes... 

The Gibbs Ensemble MC simulation methodology [17-19] enables direct simulations of phase equilibria in fluids. A schematic diagram of the technique is shown in Fig. 10.1. Let us consider a macroscopic system with two phases coexisting at equilibrium. Gibbs ensemble simulations are performed in two separate microscopic regions, each within periodic boundary conditions (denoted by the dashed lines in Fig. 10.1). The thermodynamic requirements for phase coexistence are that each... 

In summary, the Gibbs ensemble MC methodology provides a direct and efficient route to the phase coexistence properties of fluids, for calculations of moderate accuracy. The method has become a standard tool for the simulation community, as evidenced by the large number of applications using the method. Histogram reweighting techniques (Chap. 3) have the potential for higher accuracy, especially if... 

In this paper, we have reviewed some recent applications of the HPTMC method. We have attempted to demonstrate its versatility and usefulness with examples for Lennard-Jones fluids, asymmetric electrolytes, homopolymer solutions and blends, block copolymer and random copolymer solutions, semiflexible polymer solutions, and mixtures. For these systems, the proposed method can be orders of magnitude more efficient than traditional grand canonical or Gibbs ensemble simulation techniques. More importantly, the new method is remarkably simple and can be incorporated into existing simulation codes with minor modifications. We expect it to find widespread use in the simulation of complex, many-molecule systems. 

The Gibbs ensemble is a technique that allows one to study phase equilibria without an interface, by combining two simulations at the same time. In this method originally proposed and developed by Panagiotopoulos [50] two simulation cells are set up each cell represents one of the two phases in equilibrium with each other. In this algorithm, the total N, V, and T are held constant however, N and V vary in the separate simulation cells. The acceptance conditions for the various MC moves maintain the same chemical potential (i.e., equilibrium) in the two simulation cells. The method involves the execution of three types of MC trial moves. The first is the displacement of a randomly... 

The characteristic feature of the technique is the behaviour of the system if the overall density NIV lies in a two-phase region. For a single simulation box, both phases would appear, with an interface between them in the Gibbs ensemble, the interface free energy penalty can be avoided by the system arranging to have each phase entirely in its own box. This phase separation happens automatically during the equilibration stage of the simulation. 

Configurational bias techniques have been extended to other ensembles, in particular, to the Gibbs ensemble [38,41], a technique that allows direct simulation of phase equilibrium [45] (see introductory chapter by I. Siepmann). 

To improve the sampling of insertions of flexible molecules, such as the alkanes, the configurational-bias Monte Carlo technique [29,32-35,37,59] can be used. Configurational-bias Monte Carlo replaces the conventional random insertion of entire molecules with a scheme in which the chain molecule is inserted atom by atom such that conformations with favorable energies are preferentially found. The resulting bias of the particle-swap step in the Gibbs ensemble is removed by special acceptance rules [60,61] [compare to Eq. (3.3) of first chapter in this volume]... 

Panagiotopoulos and coworkers [51] use the same parameters as Larson for the study of phase behavior, but with two different simulation methodologies. The first technique is the Gibbs ensemble method, in which each bulk phase is simulated in a separate cell and molecules are interchanged and volumes adjusted between the two for equilibration of the system [52]. The second is a standard canonical ensemble simulation, like Larson s, but employs the configurational bias Monte Carlo method. The configurational bias Monte Carlo method is much more efficient than the ones based on reptation and other local moves but is not useful if any dynamic information is sought from the simulations. 

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